Equations are the cornerstone on which the edifice of science rests. Yet, argues Graham Farmelo, they can be as exquisite as the finest poetry.

by Graham Farmelo
The Guardian

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During a radio interview given by Philip Larkin in May 1974 to promote his High Windows collection, he pointed out that a good poem is like an onion. On the outside, both are pleasingly smooth and intriguing, and they become more and more so as their successive layers of meaning are revealed. His aim was to write the perfect onion.

The poetry of science is in some sense embodied in its great equations, and these equations can also be peeled. But their layers represent their attributes and consequences, not their meanings.

Despite the best efforts of poets and literary critics, no one has ever come up with an uncontroversial definition of a poem. No such problems beset mathematicians asked to define the term "equation". An equation is fundamentally an expression of perfect balance. For the pure mathematician, unconcerned with science, an equation is an abstract statement, having nothing to do with the real world. So when mathematicians see an equation such as y = x + 1, they think of y and x as abstract symbols, not as representing things that actually exist.

It is possible to imagine a universe in which mathematical equations have nothing to do with the workings of nature. Yet the marvellous thing is that they do. Scientists routinely cast their laws in the form of equations featuring symbols that represent quantities measurable by experimenters. It is through this symbolic representation that the equation has become one of the most powerful weapons in the scientists' armoury.

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The concept of beauty was especially important to Einstein. According to his son Hans, "He had a character more like that of an artist than of a scientist as we usually think of them. For instance, the highest praise for a good theory was not that it was correct or exact, but that it was beautiful." He once went so far as to say that "the only physical theories that we are willing to accept are the beautiful ones", taking it for granted that a good theory must agree with experiment.

Dirac was even more emphatic than Einstein in his belief in mathematical beauty as a criterion for the quality of theories. In the latter part of his career, he spent much time touring the world, giving lectures on the origins of the equation that bears his name, stressing that the pursuit of beauty had always been a lodestar as well as an inspiration. During a seminar in Moscow in 1955, when asked to summarise his philosophy of physics, he wrote on the blackboard in capital letters, "Physical laws should have mathematical beauty."

Both he and Einstein were responsible for some of the seminal equations of modern science, which, through their concision, power and fundamental simplicity, can be regarded as some of the most beautiful poetry - the most exquisite onions - of the 20th century.

· This is an edited extract from Graham Farmelo's introduction to the collection of essays, It Must Be Beautiful: Great Equations Of Modern Science (published next month by Granta, £20). To order a copy for £17 plus p&p, call the Guardian book service on 0870 066 7979.

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